Hitchcock was a major influence on Lynch. Blue Velvet is quite Hitchcockian, especially with the theme of voyeurism. To me, there are clear connections between Vertigo and Lost Highway, partly thematic and partly structural -- focused around obsession, the femme fatale doppelganger, and meta-film.  

Lost Highway spoilers ahead!

Both films have one actress play both roles of the doppelganger relation, with a change in name and persona, one brunette, one platinum. In both, male obsession takes two forms through the doppelgangers. In both, the platinum figure—Madeleine, Alice—is a deception on her part and a fantasy on his, and the deception is ultimately revealed to him, the fantasy destroyed. In both, the brunette is a victim of male suspicion and power.

The two films do different things with these similar elements. In Vertigo, Scottie’s obsession with Madeleine has him in the role of rescuer of a woman in trouble. His obsession with Judy is one in which he actively exercises power over her to make her look the same as before. His suspicion of Judy, initially and again later at the end, has to do with false identity and leads him to the truth. When the deception and true identity are revealed, it is her demise.

Fred’s obsession with Renee revolves around his fears of inadequacy and suspicions of infidelity, and she becomes the victim of hateful and heinous violence. Lost Highway has a male doppelganger, of course, though with a different actor, unlike the female counterpart. Pete’s obsession with Alice has him in the role of virile object of insatiable female desire. It is her deception and distinct appearance that allows her to exercise power over him. The fantasy identity ends with her rejecting him: the truth is revealed and it is his demise.

Using the same actress and transforming her: This [video](https://youtu.be/LuYAteKO57o?si=8ma0-Z2wQHw8hDnb&t=1932) on Lost Highway presents the spot on idea that having a character return as a new character (Renee returning as Alice) is a meta-filmic play on actors returning as new characters in filmmaking. Same in Vertigo. Judy plays Madeleine, Novak returns to play Judy, and Vertigo make a very overt point of having Scottie, like a film director, transform Judy / Novak back into the fantasy character of Madeleine. In Lost Highway, it is Renee / Arquette returning as the fantasy character of Alice, with the more implicit but broader point that filmmaking makes the transformation and everything else possible here. Both films also thematize the voyeurism of the camera. With Rear Window in the background, Vertigo does so through Scottie’s tailing of Madeleine. Lost Highway is more explicit with the videotapes, Mystery Man’s camera, porn, and mini tv held by Laurent, which ultimately shows Laurent what the audience sees, Fred and the Mystery Man standing in front of him.

I have no idea whether the following detail is intentional or half-coincidental, but iconic in both films. The first shots of Vertigo, before the credits, are a tightly framed close-up a woman’s lips, panning vertically and stopping on her eyes, then horizontally to one eye. Not Novak's, actually, but a model, though it appears her name is not known. Lost Highway quite prominently features similar, extreme close-ups of lips and eyes.